In MIMO system, the access point and the user site adopt the mode of spatial multiplexing and employ multiple antennas to obtain higher rate. Comparing to the general spatial multiplexing method, an enhanced technique is that the user site feeds back channel information to the access point, the access point uses certain pre-coding technique based on the obtained channel information, thereby improves the transmission performance.
The MIMO system obtains the channel information in several ways. IEEE 802.11n proposed a quantitative feedback beamforming matrix solution, the access point initiates a feedback request, the user site feeds back quantized beamforming matrix of the subcarriers on MIMO channel (also known as v matrix), the access point thus calculates the pre-coding matrix Qk.
For ease of describing the quantized feedback process of the V matrix, hereinafter a user site may be referred to as a transmitter, and the access point may be referred to as a receiver. The specific method of quantized feedback is shown in FIG. 1.
Step S101: the transmitter calculates the maximum value of the real part and imaginary part of the elements in subcarrier's beamforming matrix:
                                                        m              v                        ⁡                          (              k              )                                =                      max            ⁢                          {                                                                                                                  max                        ⁢                                                  {                                                                                                                                                  Re                                ⁡                                                                  (                                                                                                            v                                                                              (                                                                                  m                                          ,                                          l                                                                                )                                                                                                              ⁡                                                                          (                                      k                                      )                                                                                                        )                                                                                                                                                                                                                  m                                =                                1                                                            ,                                                              l                                =                                1                                                                                                                                                    m                                =                                                                  N                                  r                                                                                            ,                                                              l                                =                                                                  N                                  c                                                                                                                                              }                                                                    ,                                                                                                                                  max                      ⁢                                              {                                                                                                                                        Im                              ⁡                                                              (                                                                                                      v                                                                          (                                                                              m                                        ,                                        l                                                                            )                                                                                                        ⁡                                                                      (                                    k                                    )                                                                                                  )                                                                                                                                                                                                    m                              =                              1                                                        ,                                                          l                              =                              1                                                                                                                                          m                              =                                                              N                                r                                                                                      ,                                                          l                              =                                                              N                                c                                                                                                                                    }                                                                                                        }                                      ;                            (        1        )            wherein v(m,l)(k) represents the elements in v(k), Re(v(m,l)(k)) represents the real part of v(m,l)(k), Im(v(m,l)(k)) represents the imaginary part of v(m,l)(k); m is the row position reference, l is the column position reference, Nr is the maximum row number, Nc is the maximum column number, 1≦m≦Nr, 1≦l≦Nc, Nr≧1, Nc≧1, m, l, Nr and Nc are all positive integer, k is the subcarrier's position reference, which may be a serial number.
Step S102: said transmitter carries out a 3 bits quantization to the relative value
      max    ⁢                  {                              m            v                    ⁡                      (            z            )                          }                    z        =                  -                      N            SR                                      z        =                  N          SR                                m      v        ⁡          (      k      )      of mv(k), to obtain the quantized result Mv(k):
                                                        M              v                        ⁡                          (              k              )                                =                      min            ⁢                          {                              7                ,                                  ⌊                                      20                    ⁢                                                                                  ⁢                                                                  log                        10                                                                    (                                                                              max                            ⁢                                                                                          {                                                                                                      m                                    v                                                                    ⁡                                                                      (                                    z                                    )                                                                                                  }                                                                                            z                                =                                                                  -                                                                      N                                    SR                                                                                                                                                              z                                =                                                                  N                                  SR                                                                                                                                                                                                        M                              v                                                        ⁡                                                          (                              k                              )                                                                                                      )                                                                              ⌋                                            }                                      ;                            (        2        )            wherein
  max  ⁢            {                        m          v                ⁡                  (          z          )                    }              z      =              -                  N          SR                            z      =              N        SR            is the maximum amplitude value Alpha, └x┘ represents the maximum integer not exceeding x, NSR is the subscript of the maximum data subcarrier.
Step S103: said transmitter calculates the linear part Mvlin(k) of Mv(k):
                                          M            v            lin                    ⁡                      (            k            )                          =                                            max              ⁢                                                {                                                            m                      v                                        ⁡                                          (                      z                      )                                                        }                                                  z                  =                                      -                                          N                      SR                                                                                        z                  =                                      N                    SR                                                                                      10                                                                    M                    v                                    ⁡                                      (                    k                    )                                                  /                20                                              .                                    (        3        )            
Step S104: said transmitter carries out respectively Nb bits quantization to the real part and the imaginary part of every element in matrix V(k):
                              v                      (                          m              ,              l                        )                                q            ⁡                          (              R              )                                      =                  round          ⁡                      (                                                            Re                  ⁡                                      (                                                                  v                                                  (                                                      m                            ,                            l                                                    )                                                                    ⁡                                              (                        k                        )                                                              )                                                                                        M                    v                    lin                                    ⁡                                      (                    k                    )                                                              ⁢                              (                                                      2                                                                  N                        b                                            -                      1                                                        -                  1                                )                                      )                                              (        4        )                                          v                      (                          m              ,              l                        )                                q            ⁡                          (              I              )                                      =                              round            ⁡                          (                                                                    Im                    ⁡                                          (                                                                        v                                                      (                                                          m                              ,                              l                                                        )                                                                          ⁡                                                  (                          k                          )                                                                    )                                                                                                  M                      v                      lin                                        ⁡                                          (                      k                      )                                                                      ⁢                                  (                                                            2                                                                        N                          b                                                -                        1                                                              -                    1                                    )                                            )                                .                                    (        5        )            
Step S105: said transmitter feeds back Alpha, Mv(k) and the quantized beamforming matrix Vq(k) to the receiver.
Step S106: said receiver receives Alpha, Mv(k) and Vq(k).
Step S107: said receiver calculates the linear value according to Mv(k):r(k)=10Mv(k)/20  (6).
Step S108: said receiver carries out a zooming of the real part v(m,l)q(R)(k) and the imaginary part v(m,l)q(l)(k) of the elements v(m,l)q(k) in matrix Vq(k), to recover the beamforming matrix:
                                          Re            ⁢                          {                                                                    v                    ~                                                        (                                          m                      ,                      l                                        )                                                  ⁡                                  (                  k                  )                                            }                                =                                    max              ⁢                                                {                                                            m                      v                                        ⁡                                          (                      z                      )                                                        }                                                  z                  =                                      -                                          N                      SR                                                                                        z                  =                                      N                    SR                                                              ⁢                                                v                                      (                                          m                      ,                      l                                        )                                                        q                    ⁡                                          (                      R                      )                                                                      ⁡                                  (                  k                  )                                                                                    r                ⁡                                  (                  k                  )                                            ⁢                              (                                                      2                                                                  N                        b                                            -                      1                                                        -                  1                                )                                                    ⁢                                  ⁢                              Im            ⁢                          {                                                                    v                    ~                                                        (                                          m                      ,                      l                                        )                                                  ⁡                                  (                  k                  )                                            }                                =                                                    max                ⁢                                                      {                                                                  m                        v                                            ⁡                                              (                        z                        )                                                              }                                                        z                    =                                          -                                              N                        SR                                                                                                  z                    =                                          N                      SR                                                                      ⁢                                                      v                                          (                                              m                        ,                        l                                            )                                                              q                      ⁡                                              (                        I                        )                                                                              ⁡                                      (                    k                    )                                                                                                r                  ⁡                                      (                    k                    )                                                  ⁢                                  (                                                            2                                                                        N                          b                                                -                        1                                                              -                    1                                    )                                                      .                                              (        7        )            
According to the receiver's decoding process (Equation 7) of the quantized v matrix, the receiver gets that, the feedback overhead needed in the v matrix quantization feedback is the sum of the bit number of Alpha, Mv(k) and vq(k): NAlpha+3+2×Nb×Nr×Nc 